{-# LANGUAGE NoImplicitPrelude #-}{-# LANGUAGE DeriveGeneric #-}{-# LANGUAGE GeneralizedNewtypeDeriving #-}{-# LANGUAGE PolyKinds #-}{-# LANGUAGE ScopedTypeVariables #-}-- | Auxilary definitions for 'Semigroup'---- This module provides some @newtype@ wrappers and helpers which are-- reexported from the "Data.Semigroup" module or imported directly-- by some other modules.---- This module also provides internal definitions related to the-- 'Semigroup' class some.---- This module exists mostly to simplify or workaround import-graph-- issues; there is also a .hs-boot file to allow "GHC.Base" and other-- modules to import method default implementations for 'stimes'---- @since 4.11.0.0moduleData.Semigroup.InternalwhereimportGHC.Base hiding(Any)importGHC.Enum importGHC.Num importGHC.Read importGHC.Show importGHC.Generics importGHC.Real -- | This is a valid definition of 'stimes' for an idempotent 'Semigroup'.---- When @x <> x = x@, this definition should be preferred, because it-- works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).stimesIdempotent ::Integral b =>b ->a ->a stimesIdempotent :: b -> a -> a
stimesIdempotent b
n a
x |b
n b -> b -> Bool
forall a. Ord a => a -> a -> Bool
<=b
0=[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace [Char]
"stimesIdempotent: positive multiplier expected"|Bool
otherwise =a
x -- | This is a valid definition of 'stimes' for an idempotent 'Monoid'.---- When @mappend x x = x@, this definition should be preferred, because it-- works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)stimesIdempotentMonoid ::(Integral b ,Monoid a )=>b ->a ->a stimesIdempotentMonoid :: b -> a -> a
stimesIdempotentMonoid b
n a
x =caseb -> b -> Ordering
forall a. Ord a => a -> a -> Ordering
compareb
n b
0ofOrdering
LT->[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace [Char]
"stimesIdempotentMonoid: negative multiplier"Ordering
EQ->a
forall a. Monoid a => a
mempty Ordering
GT->a
x -- | This is a valid definition of 'stimes' for a 'Monoid'.---- Unlike the default definition of 'stimes', it is defined for 0-- and so it should be preferred where possible.stimesMonoid ::(Integral b ,Monoid a )=>b ->a ->a stimesMonoid :: b -> a -> a
stimesMonoid b
n a
x0 =caseb -> b -> Ordering
forall a. Ord a => a -> a -> Ordering
compareb
n b
0ofOrdering
LT->[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace [Char]
"stimesMonoid: negative multiplier"Ordering
EQ->a
forall a. Monoid a => a
mempty Ordering
GT->a -> b -> a
forall a a. (Integral a, Monoid a) => a -> a -> a
f a
x0 b
n wheref :: a -> a -> a
f a
x a
y |a -> Bool
forall a. Integral a => a -> Bool
even a
y =a -> a -> a
f (a
x a -> a -> a
forall a. Monoid a => a -> a -> a
`mappend` a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)|a
y a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==a
1=a
x |Bool
otherwise =a -> a -> a -> a
forall a a. (Integral a, Monoid a) => a -> a -> a -> a
g (a
x a -> a -> a
forall a. Monoid a => a -> a -> a
`mappend` a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)a
x -- See Note [Half of y - 1]g :: a -> a -> a -> a
g a
x a
y a
z |a -> Bool
forall a. Integral a => a -> Bool
even a
y =a -> a -> a -> a
g (a
x a -> a -> a
forall a. Monoid a => a -> a -> a
`mappend` a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)a
z |a
y a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==a
1=a
x a -> a -> a
forall a. Monoid a => a -> a -> a
`mappend` a
z |Bool
otherwise =a -> a -> a -> a
g (a
x a -> a -> a
forall a. Monoid a => a -> a -> a
`mappend` a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)(a
x a -> a -> a
forall a. Monoid a => a -> a -> a
`mappend` a
z )-- See Note [Half of y - 1]-- this is used by the class definitionin GHC.Base;-- it lives here to avoid cyclesstimesDefault ::(Integral b ,Semigroup a )=>b ->a ->a stimesDefault :: b -> a -> a
stimesDefault b
y0 a
x0 |b
y0 b -> b -> Bool
forall a. Ord a => a -> a -> Bool
<=b
0=[Char] -> a
forall a. [Char] -> a
errorWithoutStackTrace [Char]
"stimes: positive multiplier expected"|Bool
otherwise =a -> b -> a
forall a a. (Integral a, Semigroup a) => a -> a -> a
f a
x0 b
y0 wheref :: a -> a -> a
f a
x a
y |a -> Bool
forall a. Integral a => a -> Bool
even a
y =a -> a -> a
f (a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
<> a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)|a
y a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==a
1=a
x |Bool
otherwise =a -> a -> a -> a
forall a a. (Integral a, Semigroup a) => a -> a -> a -> a
g (a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
<> a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)a
x -- See Note [Half of y - 1]g :: a -> a -> a -> a
g a
x a
y a
z |a -> Bool
forall a. Integral a => a -> Bool
even a
y =a -> a -> a -> a
g (a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
<> a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)a
z |a
y a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==a
1=a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
<> a
z |Bool
otherwise =a -> a -> a -> a
g (a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
<> a
x )(a
y a -> a -> a
forall a. Integral a => a -> a -> a
`quot` a
2)(a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
<> a
z )-- See Note [Half of y - 1]{- Note [Half of y - 1]
 ~~~~~~~~~~~~~~~~~~~~~
 Since y is guaranteed to be odd and positive here,
 half of y - 1 can be computed as y `quot` 2, optimising subtraction away.
-}stimesMaybe ::(Integral b ,Semigroup a )=>b ->Maybe a ->Maybe a stimesMaybe :: b -> Maybe a -> Maybe a
stimesMaybe b
_Maybe a
Nothing =Maybe a
forall a. Maybe a
Nothing stimesMaybe b
n (Just a
a )=caseb -> b -> Ordering
forall a. Ord a => a -> a -> Ordering
compareb
n b
0ofOrdering
LT->[Char] -> Maybe a
forall a. [Char] -> a
errorWithoutStackTrace [Char]
"stimes: Maybe, negative multiplier"Ordering
EQ->Maybe a
forall a. Maybe a
Nothing Ordering
GT->a -> Maybe a
forall a. a -> Maybe a
Just (b -> a -> a
forall a b. (Semigroup a, Integral b) => b -> a -> a
stimes b
n a
a )stimesList ::Integral b =>b ->[a ]->[a ]stimesList :: b -> [a] -> [a]
stimesList b
n [a]
x |b
n b -> b -> Bool
forall a. Ord a => a -> a -> Bool
<b
0=[Char] -> [a]
forall a. [Char] -> a
errorWithoutStackTrace [Char]
"stimes: [], negative multiplier"|Bool
otherwise =b -> [a]
forall t. (Eq t, Num t) => t -> [a]
rep b
n whererep :: t -> [a]
rep t
0=[]rep t
i =[a]
x [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ t -> [a]
rep (t
i t -> t -> t
forall a. Num a => a -> a -> a
- t
1)-- | The dual of a 'Monoid', obtained by swapping the arguments of 'mappend'.---- >>> getDual (mappend (Dual "Hello") (Dual "World"))-- "WorldHello"newtypeDual a =Dual {Dual a -> a
getDual ::a }deriving(Eq-- ^ @since 2.01,Ord-- ^ @since 2.01,Read -- ^ @since 2.01,Show -- ^ @since 2.01,Bounded -- ^ @since 2.01,Generic -- ^ @since 4.7.0.0,Generic1 -- ^ @since 4.7.0.0)-- | @since 4.9.0.0instanceSemigroup a =>Semigroup (Dual a )whereDual a
a <> :: Dual a -> Dual a -> Dual a
<> Dual a
b =a -> Dual a
forall a. a -> Dual a
Dual (a
b a -> a -> a
forall a. Semigroup a => a -> a -> a
<> a
a )stimes :: b -> Dual a -> Dual a
stimes b
n (Dual a
a )=a -> Dual a
forall a. a -> Dual a
Dual (b -> a -> a
forall a b. (Semigroup a, Integral b) => b -> a -> a
stimes b
n a
a )-- | @since 2.01instanceMonoid a =>Monoid (Dual a )wheremempty :: Dual a
mempty =a -> Dual a
forall a. a -> Dual a
Dual a
forall a. Monoid a => a
mempty -- | @since 4.8.0.0instanceFunctor Dual wherefmap :: (a -> b) -> Dual a -> Dual b
fmap =(a -> b) -> Dual a -> Dual b
coerce-- | @since 4.8.0.0instanceApplicative Dual wherepure :: a -> Dual a
pure =a -> Dual a
forall a. a -> Dual a
Dual <*> :: Dual (a -> b) -> Dual a -> Dual b
(<*>) =Dual (a -> b) -> Dual a -> Dual b
coerce-- | @since 4.8.0.0instanceMonad Dual whereDual a
m >>= :: Dual a -> (a -> Dual b) -> Dual b
>>= a -> Dual b
k =a -> Dual b
k (Dual a -> a
forall a. Dual a -> a
getDual Dual a
m )-- | The monoid of endomorphisms under composition.---- >>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")-- >>> appEndo computation "Haskell"-- "Hello, Haskell!"newtypeEndo a =Endo {Endo a -> a -> a
appEndo ::a ->a }deriving(Generic -- ^ @since 4.7.0.0)-- | @since 4.9.0.0instanceSemigroup (Endo a )where<> :: Endo a -> Endo a -> Endo a
(<>) =((a -> a) -> (a -> a) -> a -> a) -> Endo a -> Endo a -> Endo a
coerce((a -> a) -> (a -> a) -> a -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
(.) ::(a ->a )->(a ->a )->(a ->a ))stimes :: b -> Endo a -> Endo a
stimes =b -> Endo a -> Endo a
forall b a. (Integral b, Monoid a) => b -> a -> a
stimesMonoid -- | @since 2.01instanceMonoid (Endo a )wheremempty :: Endo a
mempty =(a -> a) -> Endo a
forall a. (a -> a) -> Endo a
Endo a -> a
forall a. a -> a
id -- | Boolean monoid under conjunction ('&&').---- >>> getAll (All True <> mempty <> All False)-- False---- >>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))-- FalsenewtypeAll =All {All -> Bool
getAll ::Bool}deriving(Eq-- ^ @since 2.01,Ord-- ^ @since 2.01,Read -- ^ @since 2.01,Show -- ^ @since 2.01,Bounded -- ^ @since 2.01,Generic -- ^ @since 4.7.0.0)-- | @since 4.9.0.0instanceSemigroup All where<> :: All -> All -> All
(<>) =(Bool -> Bool -> Bool) -> All -> All -> All
coerceBool -> Bool -> Bool
(&&)stimes :: b -> All -> All
stimes =b -> All -> All
forall b a. (Integral b, Monoid a) => b -> a -> a
stimesIdempotentMonoid -- | @since 2.01instanceMonoid All wheremempty :: All
mempty =Bool -> All
All Bool
True-- | Boolean monoid under disjunction ('||').---- >>> getAny (Any True <> mempty <> Any False)-- True---- >>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))-- TruenewtypeAny =Any {Any -> Bool
getAny ::Bool}deriving(Eq-- ^ @since 2.01,Ord-- ^ @since 2.01,Read -- ^ @since 2.01,Show -- ^ @since 2.01,Bounded -- ^ @since 2.01,Generic -- ^ @since 4.7.0.0)-- | @since 4.9.0.0instanceSemigroup Any where<> :: Any -> Any -> Any
(<>) =(Bool -> Bool -> Bool) -> Any -> Any -> Any
coerceBool -> Bool -> Bool
(||)stimes :: b -> Any -> Any
stimes =b -> Any -> Any
forall b a. (Integral b, Monoid a) => b -> a -> a
stimesIdempotentMonoid -- | @since 2.01instanceMonoid Any wheremempty :: Any
mempty =Bool -> Any
Any Bool
False-- | Monoid under addition.---- >>> getSum (Sum 1 <> Sum 2 <> mempty)-- 3newtypeSum a =Sum {Sum a -> a
getSum ::a }deriving(Eq-- ^ @since 2.01,Ord-- ^ @since 2.01,Read -- ^ @since 2.01,Show -- ^ @since 2.01,Bounded -- ^ @since 2.01,Generic -- ^ @since 4.7.0.0,Generic1 -- ^ @since 4.7.0.0,Num -- ^ @since 4.7.0.0)-- | @since 4.9.0.0instanceNum a =>Semigroup (Sum a )where<> :: Sum a -> Sum a -> Sum a
(<>) =(a -> a -> a) -> Sum a -> Sum a -> Sum a
coerce(a -> a -> a
forall a. Num a => a -> a -> a
(+) ::a ->a ->a )stimes :: b -> Sum a -> Sum a
stimes b
n (Sum a
a )=a -> Sum a
forall a. a -> Sum a
Sum (b -> a
forall a b. (Integral a, Num b) => a -> b
fromIntegral b
n a -> a -> a
forall a. Num a => a -> a -> a
* a
a )-- | @since 2.01instanceNum a =>Monoid (Sum a )wheremempty :: Sum a
mempty =a -> Sum a
forall a. a -> Sum a
Sum a
0-- | @since 4.8.0.0instanceFunctor Sum wherefmap :: (a -> b) -> Sum a -> Sum b
fmap =(a -> b) -> Sum a -> Sum b
coerce-- | @since 4.8.0.0instanceApplicative Sum wherepure :: a -> Sum a
pure =a -> Sum a
forall a. a -> Sum a
Sum <*> :: Sum (a -> b) -> Sum a -> Sum b
(<*>) =Sum (a -> b) -> Sum a -> Sum b
coerce-- | @since 4.8.0.0instanceMonad Sum whereSum a
m >>= :: Sum a -> (a -> Sum b) -> Sum b
>>= a -> Sum b
k =a -> Sum b
k (Sum a -> a
forall a. Sum a -> a
getSum Sum a
m )-- | Monoid under multiplication.---- >>> getProduct (Product 3 <> Product 4 <> mempty)-- 12newtypeProduct a =Product {Product a -> a
getProduct ::a }deriving(Eq-- ^ @since 2.01,Ord-- ^ @since 2.01,Read -- ^ @since 2.01,Show -- ^ @since 2.01,Bounded -- ^ @since 2.01,Generic -- ^ @since 4.7.0.0,Generic1 -- ^ @since 4.7.0.0,Num -- ^ @since 4.7.0.0)-- | @since 4.9.0.0instanceNum a =>Semigroup (Product a )where<> :: Product a -> Product a -> Product a
(<>) =(a -> a -> a) -> Product a -> Product a -> Product a
coerce(a -> a -> a
forall a. Num a => a -> a -> a
(*) ::a ->a ->a )stimes :: b -> Product a -> Product a
stimes b
n (Product a
a )=a -> Product a
forall a. a -> Product a
Product (a
a a -> b -> a
forall a b. (Num a, Integral b) => a -> b -> a
^ b
n )-- | @since 2.01instanceNum a =>Monoid (Product a )wheremempty :: Product a
mempty =a -> Product a
forall a. a -> Product a
Product a
1-- | @since 4.8.0.0instanceFunctor Product wherefmap :: (a -> b) -> Product a -> Product b
fmap =(a -> b) -> Product a -> Product b
coerce-- | @since 4.8.0.0instanceApplicative Product wherepure :: a -> Product a
pure =a -> Product a
forall a. a -> Product a
Product <*> :: Product (a -> b) -> Product a -> Product b
(<*>) =Product (a -> b) -> Product a -> Product b
coerce-- | @since 4.8.0.0instanceMonad Product whereProduct a
m >>= :: Product a -> (a -> Product b) -> Product b
>>= a -> Product b
k =a -> Product b
k (Product a -> a
forall a. Product a -> a
getProduct Product a
m )-- | Monoid under '<|>'.---- >>> getAlt (Alt (Just 12) <> Alt (Just 24))-- Just 12---- >>> getAlt $ Alt Nothing <> Alt (Just 24)-- Just 24---- @since 4.8.0.0newtypeAlt f a =Alt {Alt f a -> f a
getAlt ::f a }deriving(Generic -- ^ @since 4.8.0.0,Generic1 -- ^ @since 4.8.0.0,Read -- ^ @since 4.8.0.0,Show -- ^ @since 4.8.0.0,Eq-- ^ @since 4.8.0.0,Ord-- ^ @since 4.8.0.0,Num -- ^ @since 4.8.0.0,Enum -- ^ @since 4.8.0.0,Monad -- ^ @since 4.8.0.0,MonadPlus -- ^ @since 4.8.0.0,Applicative -- ^ @since 4.8.0.0,Alternative -- ^ @since 4.8.0.0,Functor -- ^ @since 4.8.0.0)-- | @since 4.9.0.0instanceAlternative f =>Semigroup (Alt f a )where<> :: Alt f a -> Alt f a -> Alt f a
(<>) =(f a -> f a -> f a) -> Alt f a -> Alt f a -> Alt f a
coerce(f a -> f a -> f a
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
(<|>) ::f a ->f a ->f a )stimes :: b -> Alt f a -> Alt f a
stimes =b -> Alt f a -> Alt f a
forall b a. (Integral b, Monoid a) => b -> a -> a
stimesMonoid -- | @since 4.8.0.0instanceAlternative f =>Monoid (Alt f a )wheremempty :: Alt f a
mempty =f a -> Alt f a
forall k (f :: k -> *) (a :: k). f a -> Alt f a
Alt f a
forall (f :: * -> *) a. Alternative f => f a
empty